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Bicyclic Groups

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Blocks of Finite Groups and Their Invariants

Part of the book series: Lecture Notes in Mathematics ((LNM,volume 2127))

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Abstract

Bicyclic groups are a natural generalization of metacyclic groups. Here bicyclic means that the group can be written as a product of two cyclic subgroups. In this chapter we classify all saturated fusion systems on bicyclic groups. For odd primes, every bicyclic group is metacyclic and the classification is due to Stancu. In case p = 2 the classification is very delicate. As an application we verify Olsson’s Conjecture for blocks with bicyclic defect groups.

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  1. Institut für Mathematik, Friedrich-Schiller-Universität Jena, Jena, Germany

    Benjamin Sambale

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  1. Benjamin Sambale
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Sambale, B. (2014). Bicyclic Groups. In: Blocks of Finite Groups and Their Invariants. Lecture Notes in Mathematics, vol 2127. Springer, Cham. https://doi.org/10.1007/978-3-319-12006-5_10

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